Q2) a) The function defined by b) The equation (1) f(x, y) = e x +...

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Q2) a) The function defined by b) The equation (1) f(x, y) = e x + xy + y = 1 (ii) takes on a minimum and a maximum value along the curve Give two extreme points (x,y). (1+z)e = (1+y)e* is satisfied along the line y=x Determine a critical point on this line at which the equation is locally uniquely solvable neither for x not for y How does the solution set of the equation look like in the vicinity of this critical point? Note on (ii) use Taylor expansion upto degree 2 Q2) a) The function defined by b) The equation (1) f(x, y) = e x + xy + y = 1 (ii) takes on a minimum and a maximum value along the curve Give two extreme points (x,y). (1+z)e = (1+y)e* is satisfied along the line y=x Determine a critical point on this line at which the equation is locally uniquely solvable neither for x not for y How does the solution set of the equation look like in the vicinity of this critical point? Note on (ii) use Taylor expansion upto degree 2